In which case women won't use them. That's the literal point of the post you replied to. Anyone who wants to offer a neutral space can still do so, they just have to do so in addition to single sex spaces. And people who only want to offer single sex provisions can also do so.(subject to other discrimination rules of course).
You are thinking about the thought experiment backwards from the endpoint of gender neutral spaces continuing to exist and saying in that case they will still have the same problems because of men, but the story I was proposing as the thought experiment runs the other way (obviously! Time has to run beginning to end not vice versa!) : once single sex provisions are also an option again, we would only get to an endpoint where gender neutral spaces are wanted, used, even preferred if those spaces work for women as well, because the women would have a choice.
Once women, including those who currently do not identify as such, have a choice and can vote with their feet as to whether each individual gender neutral option on offer works for them or not, the only gender neutral options that will survive are ones that work for women.
And again, thought experiment. I'm not saying this will happen, or even that it should happen. I'm just saying the catastrophising about people caught up in genderism having no place to feel they belong is only one possible outcome; other futures are also available.